Process philosophy commonly rejects the classic conception of the principle of non-contradiction. The principle asserts that a proposition cannot be both truth and false in the same respect at the same time. I will sketch some arguments about how this might proceed.
One way to reject this is to note that it treats time as an atomic or determinate unit and as capable of being self-same. Presuming that a temporal process insists on the reality of the past and future in the present, if an event is such in virtue of its real relations to a past and a future, then it cannot be said that there is any determinate unity to the notion “same time.” If self-sameness must be absolute, then the present as a moment of change cannot be absolute, because the present is indeterminate and cannot be self-same. If the present were treated as fully determinate, then either no change has occurred, or we are treating time as a continuous slab of determinacy throughout history that belies the notion of real change. If anything is fully determinate, it is the past, but the past cannot be the basis for self-sameness in the present without admitting the real relation of the present to the past. But then the the self-sameness that is the basis for it being the same time, i.e., the past, is self-same in virtue of what is not self-same, i.e., the present. So far, I have sketched two arguments about how an event cannot be a “same time” such that the principle of non-contradiction applies. That is, the present is not self-same, and though the past is prima facie self-same, it contributes its similarity only in virtue of the present indeterminacy. Finally, the future cannot be the basis of self-similarity, because the future qua future is not actual but possible. It cannot be determinate unless once again we deny change. Perhaps I should remind the reader that I also argue for the reality of chance, which foils some but perhaps not all inventive rebuttals. To put it another way, I am arguing against a mechanistic or block universe in which one could say something very similar to what I write here, but the principle of non-contradiction may be preserved.
There is another way to reject the standard reading of the principle of non-contradiction. One could deny the principle of the excluded middle and claim that that the proposition in question is neither true nor false in the moment of change. When I invoked indeterminacy in the previous argument, this way also comes into play.
As I frequently do, here I am working through these issues on my own, and a person looking for deeper insight should probably consult Hartshorne. Sorry Whiteheadians, but Hartshorne is more readable....